King-Tim Mak

A modified Lin-Kernighan traveling-salesman heuristic

The classic Lin-Kernighan traveling-salesman heuristic is modified so that the scope of its depth search is widened. The modification yields a simple yet effective heuristic that can be easily coded and adapted for general OR applications.

Distances between traveling salesman tours

Two metrics, based respectively on k-OPT and 2-OPT, for measuring the distance between traveling salesman tours are considered and their relationship worked out.

Coherent Continuous Systems and the Generalized Functional Equation of Associativity

A theory of coherent continuous systems is outlined. Systems are to be decomposed hierarchically into modules. For this purpose, some results on the structure of continuous functions are adapted to generalize the classic 3-Modules Theorem of binary systems. Consideration of the modular structure of coherent continuous systems leads naturally to the generalized functional equation of associativity Ggu, v, w = Hu, hv, w involving four unknown 2-place continuous functions. The functional equation is solved under some regularity conditions motivated by the properties of coherent continuous systems. The solutions obtained give rise to generalized notions of parallel and series system structures.

Notes on separable preferences

Abstract Examples are constructed to show that Gormans important basic theorem for overlapping strictly separable sectors does not hold if the sectors are only nonstrictly separable. This is done with the help of a new definition for the notion of nonstrict separability of utility preferences. The new definition is equivalent to that of Bliss; but it clarifies the relationship between the geometry and representation of preferences with separable sectors. The gained geometric insight leads to the conjecture that if all sectors are strictly essential, then Gormans Basic Theorem would hold.

Using the thread-fabric perspective to analyze industry dynamics

Introduction Rapid advances in technology pose severe challenges to organizations that are dependent on their technology for day-to-day operations as well as strategic renewal. For example, one major challenge is the decision of which new technology to adopt and when to adopt it. If an organization implements a technology too early and its industry takes up another technology later as the standard, the organization will have wasted resources and must expend more in order to switch or make its technology compatible. If the organization waits for a standard to emerge, it will lose any benefits of being the first mover. Organizations struggle to predict the shape of tomorrows industry, especially more dynamic industries like wireless communications. Current business theories are limited in their ability to explain phenomena happening in these dynamic industries. They are also weak in their ability to predict the totality of these types of industries. Theories like the resource-based view of the firm and dynamic capabilities can assess an individual firms competitiveness and analyze competition between one firm and another under preordained and well-ordered industrial structures, but they cannot explain the total shape of an industry and the positioning of firms within the industry. For example, the analysis and comparison of organizations in the wireless industry, such as Nokia, Samsung, Qualcomm, Vodafone, Hutchison, and Verizon, can assess a companys resources and capabilities and its superiority over another in its resources or capabilities. But these theories do not explain the whole picture of the industry, why companies are pursuing different technologies, why and how they ally with one another, or how companies with fewer resources or capabilities can compete with those with more, for example. They also fail to account for how organizations and industries change constantly through internal and external forces. In fairly static industries like the traditional auto industry, companies operated on the same stable supply chains and other systems for decades, thus it was fair to detach two or more organizations from the same shared industrial context to compare them. However, we cannot separate organizations from their industrial context in current dynamic industries like information technology, because organizations and the industry in which they belong co-evolve rapidly by affecting each other. None of the standard business theories can give us clear answers to how, for example, Qualcomm and Korean electronics companies, that started with few resources, capabilities and market share, could create and then expand their territory in the GSM-dominated wireless industry led by Nokia. More broadly, the nature of modern business competition appears to be undergoing a fundamental change. To explore the new industrial dynamics, we use the intuitive ideas of threads, fabric and weaving to develop a perspective which promises to greatly facilitate the description and analysis of highly competitive and dynamic industries such as the wireless industry. The Thread-Fabric view perceives organizations and industries as organic entities rather than as rigid and mechanical units. The proposed perspective also differs from existing theories in that it allows a way to observe industries and predict the future not only at the level of individual firms but also from the scope of entire industries. For industry, we hope this theory can support managers and decision-makers to understand the fast-changing business environment and build strategies and tactics to achieve their business goals. For academia, we hope our proposal shows a new way to analyze and understand how industries transform in this day and age. Here, we describe our framework and clarify its details by applying it to the example of the global wireless industry. We use this framework to analyze current dynamics in the wireless industry: the fight for third-generation technology standards, and within that, the competition over wireless internet platform standards. We also discuss the possible use of this framework to predict future directions in industries.

A note on Barlow-Wu structure functions

The essential feature of the class of Barlow-Wu continuum structure functions is revealed through a new axiomatic characterization. The axioms introduced facilitate ready determination of whether a Barlow-Wu function is an appropriate model for a particular system.

Separability and the Existence of Aggregates

If a continuous real-valued function Φ in n variables x1,...,xn has the representation

Standardization as a knowledge game

\Phi ({x_1},...,{x_n}) = F(f({x_{1,...,}}{x_k}),{x_{k + 1}},...,{x_n})